Book Description :
Genre Educational, Economics & Finance
Written By : Patrick Roger
Book Size 6.45 Mb
This book and its companion (part I) present the elements of analysis and linear algebra used in financial models and in microeconomics. Functions of one and several variables and matrices are developed in part I and vector spaces, linear mappings and optimization methods are developed in part II. Instead of formal proofs as in mathematical books, we develop examples and economic illustrations of the use of the concepts presented in the book. The books complement “Probability in Finance” and “Stochastic Processes in Finance” providing a broad overview of the mathematics of financial models.
Content :
Introduction
Vector spaces and linear mappings
Vector spaces: definitions and general properties
Linear mappings
Finite-dimensional spaces and matrices
Norms and inner products
Hilbert spaces
Separation theorems and Farkas lemma
Functions of several variables
Metric spaces
Continuity and differentiability
Implicit and homogeneous functions
Optimization without constraints
Preliminaries
Optimizing a single-variable function
Optimizing a function of two variables
Functions of n variables
Constrained optimization
Functions of two variables and equality constraint
Functions of p variables with m equality constraints
Functions of p variables with mixed constraints
Index
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